Abstract. This paper presents a new algorithm for conductivity imaging. Our idea is to extract more information about the conductivity distribution from data that have been enriched by coupling impedance electrical measurements to localized elastic perturbations. Using asymptotics of the elds in the presence of small volume inclusions, we relate the pointwise values of the energy density to the measured data, through a nonlinear PDE. Our algorithm is based on this PDE and takes full advantage of the enriched data. We give numerical examples that illustrate the performance and the accuracy of our approach.

Abstract.We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.Mathematics Subject Classification. 35J20, 35B27, 35R30.

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This paper is concerned with the homogenization of an eigenvalue problem in a periodic heterogeneous domain for the multigroup neutron di usion system. Such a model is used for studying the criticality of nuclear reactor cores. We prove that the rst eigenvector of the multigroup system in the periodicity cell controls the oscillatory behavior of the solutions, whereas the global trend is asymptotically given by a homogenized di usion eigenvalue problem. The neutron ux, corresponding to the rst eigenvector of the multigroup system, tends to the product of the rst periodic and homogenized eigenvectors. This result justi es and improves the engineering procedure used in practice for nuclear reactor core computation.